Justify is the 13th horse to win the Triple Crown. That alone puts him in exclusive company. His dominance rating for the three Triple Crown races, however, ranks Justify at the bottom of the list of those 13.

The reason is the horse’s relatively small margins of victory in the races, particularly the Preakness. Justify won the three Triple Crown races by a total of 4.75 lengths. With the exception of 1978 Triple Crown winner Affirmed, that equals the smallest cumulative margin of victory of any Triple Crown horse. And the 1978 Triple Crown series is unique because in all three races Affirmed staged tight duels with another exceptional horse, Alydar, who finished second by 1.5 lengths, a neck and a head respectively. The shared dominance of those two horses is demonstrated by the margins separating Affirmed and Alydar from the third place finisher, 33.5 lengths and 30.75 lengths respectively.

The largest cumulative margin of victory by any Triple Crown winner was the 36 lengths, both by 1973 Triple Crown winner Secretariat and by 1943 champion Count Fleet. Famously, 31 of Secretariat’s 36-length margin was provided in the final leg of the Triple Crown, the Belmont. Count Fleet won his Belmont by 25 lengths.

When American Pharoah won the 2015 Triple Crown, his victory margins were 1 length in the Kentucky Derby, 7 lengths in the Preakness and 5.5 lengths in the Belmont.

Justify’s -0.74 dominance rating in the Preakness matches the weakest dominance rating by any Triple Crown winner in a single race. Gallant Fox posted a -0.74 dominance rating in the 1930 Belmont to wrap up the Triple Crown. In thoroughbred racing negative Z Scores are good.

Here is the ranking of the 13 Triple Crown winners based on the cumulative total of the Z Scores of their performances in the three Triple Crown races:

Ariya Jutanugarn’s June playoff victory in the 2018 U.S. Women’s Open ranks among the 20 most dominant performances in the event’s more than 70 year history.

Jutanugarn, who is from Thailand, compiled a Z Score of -2.56 in defeating South Korea’s Hyo Joo Kim on the fourth hole of their playoff. It was Jutanugarn’s second major victory; she also won the 2016 British Open.

Her -2.56 Z score ranks in a three-way tie for 14th best in the history of the Women’s Open. Others who compiled a -2.56 Z Score were Louise Suggs in 1949 and Karrie Webb in 2000. Jutanugarn’s performance was the best in a Women’ Open since 2013, when Inbee Park won with a -2.77 Z Score.

As good as Jutanugarn’s performance was, it might have been better. She began the final nine holes at -16, holding a seven-stroke lead. Had she shot even par on the final nine, she would have posted a -3.32 Z Score, and that would have been the second best in the tournament’s history.

Here are the 25 best performances, measured by Z Score, in the history of the U.S. Women ‘s Open:

As he has routinely been for much of the past decade, Washington’s Alex Ovechkin was the NHL’s most exceptional goal scorer again in 2017-18. This year, however, his league-leading 47 goals scored didn’t quite measure up to his other recent seasons.

Ovechkin’s total translated to a 3.10 Z Score among the season’s top 60 goal producers. It was the fifth time since 2012-13 and seventh time overall that Ovechkin has produced the best Z Score among goal producers. But it was also his lowest Z Score among those seven league-leading seasons, although it was also a higher Z Score than any produced by any other NHL goal-scorer since Tampa Bay’s Steven Stamkos produced a 4.62 during the 2011-12 season.

Ovechkin’s score was the 27th highest ever recorded by a goal scorer. He is already represented six times among the top 25 – three times among the top 10 – his best being a 4.23 Z Score in 2015-16 that ranks sixth all time.

Here is a list of the NHL’s 10 most exceptional goal scoring seasons of all time based on Z Score:

Brooks Koepka’s performance in his second U.S. Open victory at Shinnecock Hills in June was even more dominant than his 2017 victory.

Koepka compiled a Z Score of -2.42 in overcoming the Shinnecock challenge, fractionally more dominant than his winning -2.24 Z Score at Erin Hills in 2017.

In strokes, Koepka’s winning margin in the 2018 Open was just one stroke over Tommy Fleetwood. He won the 2017 tournament by four strokes. But the field average of the players who completed four rounds at Shinnecock was 292.35 strokes, significantly higher than the 288.12 field average for those completing four rounds at Erin Hills in 2017. The 2018 field was also much more tightly bunched, with a performance standard deviation of 4.69 strokes. The standard deviation of the field average in 2017 was 7.21 strokes, demonstrating a much more spread-out field. Both of those factors made Koepka’s 2018 performance more exceptional.

Even so, Koepka’s Z Score does not measure up with the all-time top 25 U.S. Open performances. Attaining that plateau would have required a Z Score of -2.56, a standard last attained in the Open by Martin Kaymer in 2014. Koepka’s Z Score is the best in the U.S. Open since Kaymer’s -2.81.

Here are the 10 most exceptional U.S. Open performances in history based on winning Z Score:

Methodology: Each horse’s rating is based on the standard deviation of the distance covered as of the time the winner crossed the finish line measured against the average of other race finishers unless unless a horse finished more than one-half standard deviation behind the horse immediately ahead of it. If the latter occurs, that horse’s distance and the distances of all subsequent horses are not considered. The Kentucky Derby is a 1.25 mile race, a distance that translates to 6,600 feet. In racing, distances behind the leader are measured in lengths, a measure commonly standardized at eight feet per length. Therefore, a horse finishing one length behind the winner is presumed to have covered 6,592 feet as of the time the winner crossed the finish line. The following example, from the 2015 Kentucky Derby won by Triple Crown winner American Pharoah illustrates the method. Eighteen horses started the race of which 12 finished close enough behind the leader to qualify for inclusion in the rating. The field average distance covered by those 12 was 6,544 feet; the standard deviation was 33.42 feet:

Place Horse/Jockey Lengths Distance St. Dev.

American Pharoah/Espinoza 6,600 67

Firing Line/Stevens 00 6,592 1.43

Dortmund/Garcia 00 6,576 0.95

Frosted/Rosario neck 6,574 89

Danzig Moon/Leparoux 25 6,548 0.12

Materiality/Castellano 25 6,538 -0.19

Keen Ice/Desmoreaux 00 6,530 -0.42

Mubtaahij/Soumillon 75 6,524 -0.60

Itsaknockout/Saez 75 6,518 -0.78

Carpe Diem/Velazquez 75 6,518 -0.78

Frammento/Nakatani 00 6,510 -1.02

Bolo/Bejarano 75 6,502 -1.26

Z/Vazquez 2.75

Ocho Ocho Ocho/Trujillo head

Far Right/Smith head

War Story/Talamo 50

Tencendur/Franco 75

Upstart/Ortiz 50

Summary: To dedicated race fans, the most surprising element of the following list will be the absence of more than half of the Triple Crown winners in history…among them American Pharoah, who has noted above rated 1.67. These absences are due to a variety of factors. For the record, here are the standard deviations of the performances of the other six Triple Crown winners not among the all-time top 25 Kentucky derby winners: Seattle Slew (1977) 1.67, Gallant Fox (1930) 1.66, Omaha (1935) 1.55, Sir Barton (1919) 1.52, Citation (1948) 1.27, Affirmed (1978) 1.26. An additional word about Citation, the 1948 Triple Crown winner often numbered among the greatest thoroughbreds in racing history. It is no criticism of Citation’s overall achievements to say that his Kentucky Derby performance, while victorious, was not particularly exceptional. He won by 3.5 lengths over a weak field of just six. Beyond that, the runner-up, Coaltown, was Citation’s stablemate, and Coaltown ran as a pacesetter for Citation, who passed Coaltown in the stretch and pulled away.

Disclaimer: Our perceptions of the strength of individuals (or teams) can be colored by factors that are extraneous to their actual dominance: general familiarity, the presence or absence of attention-getting personalities, national affinities, subjective opinions that become engrained over time, superiority in certain statistical categories being the most likely. This rating is based on an objective methodology, meaning that it is immune to influence from any of those criteria. That also means its findings may vary – in some cases substantially – from the historical consensus. As you scan this list, be prepared to have your presumptions of relative greatness challenged.

Each paragraph is headed by the name of the horse, year, jockey, odds and standard deviation score.

25: Determine, 1954, Raymond York, 4.3-to-1, 1.78. Going off as part of an entry pegged as the second favorite, Determine survived a jostled start to overtake Hasty Road at the head of the stretch and win going away.

24: Count Fleet, 1943, Johnny Longden, 0.4-to-1, 1.79. The overwhelming favorite based on his four victories as a two-year-old, Count Fleet assumed the lead at the outset and was never headed. Jockey Johnny Longden, who would ride County Fleet to that season’s Triple Crown, kept him well in front of eventual runner-up Blue Swords, finishing three lengths to the good.

23: California Chrome, 2014, Victor Espinoza, 2.5-to-1, 1.813. Rated close to the lead from early in the race, California Chrome moved in front around the final turn and his driving finish wore down Samraat, who faded from a challenging position to finish fifth. California Chrome beat longshot Commanding Curve by nearly two lengths. Chrome went on to win the Preakness before managing only a fourth place finish in the Belmont.

22: Thunder Gulch, 1995, Gary Stevens, 24-5-to-1, 1.822. Held just off the lead in a tightly packed field through the first mile, Thunder Gulch passed Serena’s Song at the head of the stretch and won a battle with Tejano Run for the finish line by nearly four lengths.

21: Barbaro, 2006, Edgar Prado, 6.1-to-1, 1.860. Race fans are familiar with the tragic story of Barbaro, who left the Derby as a Triple Crown favorite only to break down in the Preakness and eventually be euthanized. Only the second betting favorite when the Derby began, Barbaro stumbled at the start but caught the leaders at the far turn and reached the lead by the sixteenth pole. From there he won inspirationally, opening up a six and one-half length advantage by the finish line.

20: Proud Clarion, 1967, Ron Ussery, 30-to-1., 1.861. A 30-to-1 shot at the race’s start, Proud Clarion broke inauspiciously behind the heavy favorite, Damascus, and ran eighth at the halfway point. Forced outside as Ron Ussery positioned him for stretch run, he circled the field and caught leader Barb’s Delight and ran him down in the final furlong, winning by a length.

19: Monarchos, 2001, Jorge Chavez, 10.5-to-1, 1.873. Bumped at the start, Monarchos was pulled back at the race’s outset, standing only 10th at the three-quarter mile mark. But a strong sustained rush pulled him up to sixth at the mile mark and to second at the head of the stretch. From there he pulled away from Congaree to win by more than four lengths.

18: Pompoon, 1937, Harry Richards, 8-to-1, 1.874. Pompoon is the only horse among the 25 most dominant who did not actually win the race. He had a good excuse, running against War Admiral, a future Triple Crown winner and one of racing’s all-time great horses. This should not diminish Pompoon’s own run. Close to the pace all the way, he worked his way to second place – a length and a half behind War Admiral – by the mile mark. Although unable to catch the eventual winner, he did rout the rest of the 20-horse field, finishing eight lengths ahead of the third place finisher.

17: Unbridled, 1990, Craig Perret, 10.8-to-1, 1.927. Only the fifth betting favorite, Unbridled broke badly in a tightly packed 15-horse field and was 12th a half mile into the race. But jockey Craig Perret found running room outside entering the stretch, enabling him to tap Unbridled’s speed heading home. He won by three and one-half lengths.

16: Count Turf, 1951, Conn McCreary, 14.6-to-1, 1.931. Despite being the son of 1943 Derby winner Count Fleet and grandson of 1928 winner Reigh Count, Count Turf was so lightly regarded that he was part of a five-horse field entry. Count Turf came from fourth at the mile marker and won going away, his final margin put at four lengths.

15: Street Sense, 2007, Calvin Borel, 4.9-to-1, 1.932. The first of Calvin Borel’s three Kentucky Derby champions, Street Sense ran a conservative race that saw him 17th in a 20-horse field at the three-quarters mile mark. Running in Borel’s favorite position on the rail, Street Sense found enough running room deep on the backstretch to move all the way to third by the mile mark. He took the lead from Hard Spun at the head of the stretch and won by nearly four lengths.

Gato Del Sol, 1982, Eddie Delahoussaye, 21-to-1, 1.95. Jockey Eddie Delahussaye broke Gato Del Sol easily, positioning him at the back of a 19-horse field as late as the half mile mark. Finding ample running room on the outside, Gato Del Sol advanced easily up the backstretch, working his way to fifth by the mile mark. As the leaders faded, Gato Del Sol displayed plenty in reserve for a stretch run that saw him hold off a fast-closing Laser Light for a two and one-half length victory.

13: Always Dreaming, 2017, John Velazquez, 5-to-1, 1.96. The weak betting favorite in a 19-horse field, Always Dreaming stalked longshot State of Honor down the backstretch, gradually drew away and fought off other challengers into the home stretch. He won by two and three-quarters lengths.

12: Hill Gail, 1952, Eddie Arcaro, 1.10-to-1, 2.00. With Eddie Arcaro in the saddle, Hill Gail went off as almost an even money favorite in the field of 16, took the lead at the outset, withstood a brief challenge from Hannibal on the backstretch, then opened up a five-length lead by the mile marker. Perhaps eased a bit toward the finish, he won by two lengths.

11: Smarty Jones, 2004, Stewart Elliott, 4-to-1, 2.02. The betting favorite, Smarty Jones stalked the early leader, Lion Heart, down the backstretch, challenged him three-quarters of a mile from the finish, seized the lead with a furlong remaining and pulled away to a three-length win. He would go on to win the Preakness and then see his Triple Crown hopes dashed by a runner-up finish at the Belmont Stakes.

10: Big Brown, 2008, Kent Desormeaux, 2.4-to-1, 2.03. The heavy favorite due to a series of sensational winter and spring performances, Big Brown worked his way forward from the 20th starting position to seize the lead with a quarter mile to go. The rest was easy, Desormeaux gradually building a five-length winning margin. Like Smarty Jones, Big Brown added the Preakness and went to the Belmont Stakes a heavy favorite to complete the Triple Crown, only to finish that race well out of the money.

Reigh Count, 1928, Chick Lang, 2.06-to-1, 2.08. A dominant two-year-old, Reigh Count demonstrated why he was the clear betting favorite. Close to the front virtually from the start, he forced the leader, Misstep until overtaking him down the stretch and winning by three lengths. Reigh Count was the sire of Derby winner County Fleet and the grandfather of Derby winner Count Turf.

Twenty Grand, 1931, Charles Kurtsinger, 0.88-to-1, 2.09. Possibly the shortest favorite in Derby history, Twenty Grand broke leisurely but gained momentum entering the backstretch and began relentlessly wearing down the rest of the 12-horse field. He won by four lengths. Jockey Charles Kurtsinger would also ride Twenty Grand to a Belmont victory, and would add the Preakness in 1933. In 1937, aboard War Admiral, Kurtsinger won the Triple Crown.

7: Hoop Jr., 1945, Eddie Arcaro, 3.7-to-1, 2.11. Hoop Jr. is often overlooked today, having run in an era that also produced such racing legends as Triple Crown winners Count Fleet, Assault and Citation. Still he went to the Derby post as the second favorite in the final race of the World War II era, seized the lead early and was never headed. Arcaro’s horse opened up a six-length lead by the head of the stretch and gave none of it back.

Pensive, 1944, Conn McCreary, 7-to-1, 2.12. The 16-horse race quickly broke down into a battle between Pensive, Broadcloth and the heavy favorite, Stir Up. At the top of the stretch, Broadcloth and Stir Up staged a neck-and-neck battle, but that effort exhausted both, and Pensive overtook them in the final furlong to win by four. Pensive nearly completed the Triple Crown, adding the Preakness and finishing a close second in the Belmont. Jockey Conn McCreary would win a second Derby in 1951 aboard Count Turf.

Mine That Bird, 2009, Calvin Borel, 50-to-1, 2.13. Probably the biggest upset in Kentucky Derby history, Calvin Borel rode Mine That Bird to the Derby win despite being only the 18th betting choice in the 20-horse field. As was his pattern, Borel kept his horse well back on the inside through the race’s early stages, beginning his drive at the mile mark and slipping into the lead position at the stretch. Riding the rail toward the finish, Borel pulled away to win by nearly seven lengths.

Whirlaway, 1941, Eddie Arcaro, 3-to-1, 2.14. The betting favorite coming off a four-win season as a two-year-old, Whirlaway found himself blocked coming out of the gate. So Arcaro eased him back until asking for speed with a half mile to go. He got it; Whirlaway powered into the lead as the stretch run began and left no doubt, winning by eight lengths. He and Arcaro went on to complete the Triple Crown.

Secretariat, 1973, Ron Turcotte, 1.5-to-1, 2.15. Rated easily by Turcotte at the start, Secretariat disdained the rail for the clear outside lane, which he used to rein in his competitors down the backstretch. He caught the front-runner, Sham, just past the mile marker, and won by three lengths. Secretariat of course went on to win the Triple Crown, an achievement capped by his stunning 31-length win in the Belmont stakes.

Assault, 1946, Warren Mehrtens, 8-to-1, 2.191. The son of 1936 Kentucky Derby and Preakness winner Bold venture, Assault made his reputation with a dominant performance at the Derby. Guided by Warren Mehrtens, Assault stayed close to Spy Song until passing him for the stretch run. The final quarter mile was a pure exhibition, Assault steadily pulling away to an eight-length victory. He would go on to claim the Triple Crown.

1: War Admiral, Charles Kurtsinger, 1937, 1.6-to-1, 2.193. Son of the legendary Man O’ War, War Admiral had been lightly raced, a fact that did not deter betters from making him nearly an even-money favorite. Leading virtually start to finish, he ran easily until the final half mile when – facing a persistent challenge from Pompoon – Kurtsinger asked for speed. War Admiral maintained his two-length lead to the finish, he and Pompoon leaving the rest of the 20-horse field eight to 10 lengths and more in arrears. The subsequent Triple Crown winner, War Admiral is perhaps best-known today for his 1938 match race against Seabiscuit.

Qualifications for consideration: Eligible teams are those teams that won an NCAA Tournament championship. The tournament has been played annually since 1939; hence, with the completion of the 2018 championship a total of 80 teams are eligible for consideration.

Methodology: Each team’s rating is based on the standard deviation of its points per game differential measured against the standard deviations of the point differentials of all tournament teams. If a team’s standard deviation is one-half point or more worse than the team immediately above it, the performance of that team and all teams below it are not factored into the rating. The example below shows the scores for each team during the 1966 tournament famously won by Texas Western (now UTEP) over Kentucky. That tournament featured 22 teams, 4 of whose performance standard deviations did not meet the minimum standard for qualification. The average point differential was +5.29; the group standard deviation was 0.56.

1966 Games PPG PPGA Diff. Std Dev.

Texas Western 5 81.00 74.60 6.40 1.10

Kentucky 4 79.50 76.75 2.75 0.41

Western Kentucky 2 92.00 83.00 9.00 1.60

St. Josephs 2 69.50 62.00 7.50 1.31

Davidson 2 86.50 79.50 7.00 1.22

Syracuse 2 87.50 84.50 3.00 0.46

Utah 3 77.00 74.33 2.75 0.40

Kansas 2 78.00 75.50 2.50 0.37

Duke 3 81.67 79.33 2.33 0.34

Houston 2 71.00 69.50 1.50 0.18

Dayton 2 68.50 68.50 0.00 -0.11

Oregon State 2 63.50 65.00 -1.50 -0.39

Cincinnati 1 76.00 78.00 -2.00 -0.48

Michigan 2 78.50 81.50 -3.00 -0.67

SMU 1 70.00 76.00 -6.00 -1.24

Colorado State 1 76.00 82.00 -6.00 -1.24

Miami (Ohio) 1 51.00 58.00 -7.00 -1.43

Pacific 1 74.00 83.00 -9.00 -1.81

Oklahoma City 1 74.00 89.00 DNQ

Providence 1 48.00 65.00 DNQ

Loyola (Chicago) 1 86.00 105.00 DNQ

Rhode Island 1 65.00 95.00 DNQ

Disclaimer: Our perceptions of the strength of teams (or individuals) can be colored by factors that are extraneous to their actual dominance: general familiarity, the presence or absence of attention-getting personalities, subjective opinions that become engrained over time, superiority in certain statistical categories being the most likely. This rating is based on an objective methodology, meaning that it is immune to influence from any of those criteria. That also means its findings may vary – in some cases substantially – from the historical consensus. As you scan this list, be prepared to have your presumptions of relative greatness challenged. It is also worth noting that tournament formats such as the NCAA Tournament can yield debatable results. This is because the most reliable results are obtained in “closed-end competitions” – that is, when teams play each other – and that never occurs in single-elimination events.

In a paragraph: North Carolina went 14-2 in the ACC, entered the tournament as a No. 1 seed, and never faced a seed higher than 5 until running into fellow No. 1 seed Illinois in the championship game. In the title game, May scored 26 points and the Tar Heels shot 52 percent.

In a paragraph: Kentucky spent all but a few weeks in February atop the Associated Press poll, and never fell lower than third. The Wildcats’ only two losses came to SEC foes Alabama and Louisiana State, the latter by one point in overtime.

In a paragraph: Ranked outside the top 10 both in the pre-season and as late as early January, the Wildcats won 16 of 17 between Dec. 31 and Feb. 20. In the tournament, their only two close calls were with Kansas in the regional final and North Carolina in the championship game. In that title game, Phil Booth came off the bench to provide 20 points.

In a paragraph: Playing without their graduated star, Oscar Robertson, the Bearcats won their final 18 regular season games. Still they entered the tournament as a decided underdog to the defending champion Ohio State Buckeyes. The championship game was close throughout, Cincinnati’s defense holding Ohio State star John Havlicek to just one field goal and two points. Jerry Lucas offset that with a 27-point performance, but the deeper Bearcats prevailed.

In a paragraph: With a 30-1 record and No. 1 national ranking, the Wolfpack posed the most serious challenge to UCLA’s reign in nearly a decade. The teams met in the national semi-final ranked 1-2, the nationally televised contest pitting Wolfpack star Thompson against Bruins seniors Bill Walton and Jamaal Wilkes. Concluding his illustrious career, Walton produced 29 points and 18 rebounds. But Thompson responded with 28 points, and center Tom Burleson threw in 20 as the Wolfpack outscored UCLA 13-10 in the second overtime to end their string of seven consecutive national championships. In the title game, Thompson and Towe dominated Marquette, holding star Warrior forward Bo Ellis to just 12 points in a 76-64 Wolfpack victory.

In a paragraph: The Terrapins came into the tournament having lost only once since mid-January, and were never seriously threatened. In their championship-game victory over Indiana, Maryland led by six at halftime and built that advantage to 12 by game’s end. Dixon led the offense with 18 points, but he got strong support from Baxter (15) and Wilcox (10).

In a paragraph: Ranked among the top 5 all season, the Blue Devils defeated North Carolina in their final regular season game, rolled through the ACC Tournament, and blew away five NCAA opponents by double digit margins. In the championship game against fifth ranked Arizona, Duke broke open a close game in the second half with Dunleavy (21 points) and Battier (18) leading the way. Battier was named the tournament’s Most Outstanding Player.

In a paragraph: Lovellette, who went on to a solid professional career, is the only player to have led the nation in scoring while also leading his team to a national championship. In the title game he scored 33 points and added 17 rebounds. For his tournament efforts he was named the Most Outstanding Player. For Allen, the victory was a capstone to a career that included 37 seasons at Kansas producing 590 victories against only 219 defeats plus 22 conference championships.

In a paragraph: On their way to the first of two consecutive NCAA championships, the Gators were ranked No. 1 in pre-season polls and again from mid-January through mid-February. Between Dec. 6 and Feb. 14 they won 17 consecutive games. In the championship games Florida’s superb depth – all five starters averaged in double figures — showed through. Horford, Green, Brewer and Humphrey all posted between 13 and 18 points.

In a paragraph: The Golden Bears entered the tournament outside the top 10 rankings, but coming off a 14-2 conference season and featuring the nation’s best defense. They had allowed just 51 points per game. The tournament was more of the same. In the semi-finals, heavily favored Cincinnati’s Oscar Robertson scored 19 points, but the Bears held everyone else down and Imhoff produced 22 as Cal pulled away in the second half. Facing West Virginia and star guard Jerry West in the championship game, they built a 39-33 halftime lead and held on at the finish. West scored 28 but Newell’s defense held everyone else in check.

In a paragraph: The Wildcats entered the tournament ranked only 9th nationally. But lightly regarded Manhattan stunned top-ranked West Virginia in the tournament’s first round, second ranked Cincinnati fell to third ranked Kansas State in a regional semi-final, and Seattle took out fourth ranked San Francisco in the West Regional, then eliminated K-State in the national semi-final. That opened the door for Rupp’s Wildcats, who eliminated No. 5 Temple by a point in the semis. In the championship game, Hatton out-scored Seattle’s Elgin Baylor 30-25 and the Cats overcame a three-point halftime deficit to win going away.

In a paragraph: Top-ranked much of the season, the Tar Heels opened with 13-straight victories, and won 10 more consecutively from mid-January to mid-February. The championship game against Michigan State was no contest: Carolina opened up a 21-point halftime advantage. Lawson, Hansbrough and Ellington were all named to the all-tournament team.

In a paragraph: Undefeated and top-ranked all season, this iteration of the Bruins dynasty faced few challenges. The Bruins topped 100 points in each of their first seven games, and no regular season opponent came closer than six points. The tournament was more of the same, including eliminations of No. 5 Long Beach State by 16 points and No. 4 Louisville by 21. A hoped-for showdown between the Bruins and second ranked North Carolina evaporated when Florida State upset the Tar Heels 79-75 in their semi-final. In the championship matchup, UCLA grabbed an 11-point half time advantage and withstood a Seminole comeback. Walton scored 24 and Wilkes 23.

In a paragraph: Despite returning three starters from their championship team, the Bearcats were rated behind the Ohio State Buckeyes all season. The much sought-after championship game materialized when Cincinnati scraped past UCLA in the semi-final. In the first title game ever to pit the nation’s two top-ranked teams, the Bearcats held Buckeye stars Jerry Lucas and John Havlicek to 11 pints each and breezed to their repeat championship.

In a paragraph: The national championship game, pitting Johnson against No. 1 Indiana State’s Larry Bird, was every bit as looked-upon as their subsequent pro matchups would be. The Spartans showed the experience gleaned from their Big Ten championship, leading from the early moments. Johnson outscored Bird 24-19 and added 5 assists plus 7 rebounds. Kelser was the Spartans’ inside punch, adding 19 points and 8 rebounds.

In a paragraph: This was the first of three straight Buckeye teams to reach the championship game, and the only one to win the title. The Buckeyes won 13 consecutive games before a surprising late season thrashing at Indiana. It may have sobered them. Ohio State raced through four tournament games, winning all of them by 17 points or more. The title game against defending champion California was another blowout, Ohio State leading 37-19 at halftime. Lucas hit seven of nine field goals and the Buckeyes as a group made 31 of 46 shots, 67 percent. Lucas and Nowell were named to the all-tournament team.

In a paragraph: The defending champion Dons began the season ranked No., 1 and were never unseated from that perch. Only one team all season played them within 10 points, and that team – California – held the ball in a 33-24 defeat. They also overcame the loss of star guard K.C. Jones, whose eligibility expired just prior to the tournament. Even so, in the title game, Russell dominated, making 11 field goals and claiming 27 rebounds. Russell and Perry were obvious all-tournament choices. That summer, Russell and Jones led the U.S. Olympic team to a gold medal.

In a paragraph: The hoped-for showdown between Tarkanian’s Runnin Rebels and top-ranked Oklahoma evaporated when North Carolina took out the Sooners in the tournament’s second round. That made Tarkanian’s Rebels, with only one loss since February, the prohibitive favorites. They validated that view with a 30-point victory over Loyola Marymount in the regional championship game, then outlassed Duke by 30 to claim the national title. The Rebels shot 61 percent in that game.

1970 UCLA (2.46)

Record: 28-2.

Tournament wins: Long Beach State 88-65, Utah State 101-79, New Mexico State 93-77, Jacksonville 80-69.

In a paragraph: This was the often-overlooked “team between,” the Bruins championship club that had neither Kareem Abdul-Jabbar nor Bill Walton. More remarkably, the Bruins starters were all iron men; no reserve averaged more than two minutes of playing time per game. Even so, the Bruins sailed through their first 21 games undefeated before losing twice late in conference play. The defeats steeled them in advance of the tournament, in which no opponent played them within 10 points. Facing a once-beaten Jacksonville team that started two 7-footers for the championship, Rowe, Wicks, Patterson and Vallely all scored 15 points or more and the Bruins led pretty much all the way.

In a paragraph: The Hoosiers enjoyed one of the game’s great comeback stories. In mid-January they were an uninspired 10-7 and unranked. They went 16-2 the rest of the way, reaching the top 10 and winning their first four tournament games by margins ranging from 15 to 35 points. Facing North Carolina in the championship game, Thomas scored 23 points and the Hoosiers broke open a 27-26 game at halftime to win by 13.

In a paragraph: With Walton at his best, the six-time defending champion Bruins opened the season ranked No. 1 and were never dislodged. Their closest regular season challenges came in six point victories over Oregon State and Stanford. When second ranked North Carolina St. failed to make the tournament, experts essentially conceded the championship to UCLA, and with good reason. In the final game against Memphis, Walton played perhaps the greatest game in college basketball history. He hit 21 of 22 shots, scored 44 points and added 13 rebounds to carry the Bruins.

In a paragraph: Rediscovered due to the NCAA Tournament success of the 2018 edition of the Ramblers, the 1963 bunch deserves to be remembered for its own performance. This was one of the legitimately great teams in tournament history. Ranked second most of the season, Loyola chased the two-time defending champion Bearcats in the polls, and their tournament run was viewed in Chicago as a prelude to an inevitable showdown. That prelude included their widely recalled meeting with Mississippi State, a game laced with racial overtones given Loyola’s four black starters and the segregationist viewpoints of Mississippi’s governor at the time. The Ramblers won that won 61-51, and little more than a week later earned the right to face Cininnati for the championship. The more experienced Bearcats raced out to an early lead, but the Ramblers rallied from a 15-point deficit in the second half and tied the game on Harkness’s jumper with four seconds left. Rouse tipped in the overtime winner at the buzzer.

In a paragraph: The Bruins were ranked No. 1 all season, and only two teams came within 10 points of them. Both held the ball to keep down the score. Abdul-Jabbar, then known as Lew Alcindor, carried a 29-point per game scoring average with 15.5 rebounds per game and a 67 percent shooting average. The team’s dominance was all the more remarkable since only one key player, Warren, was an upper-classman. The tournament’s outcome was never in doubt, especially when SMU took out second-ranked Louisville in a regional semi-final. Meanwhile the Bruins opened up double digit leads by halftime in every one of their tournament games. In the title game against heavy underdog Dayton, Abdul-Jabbar scored 20 points and added 18 rebounds, Allen scored 19, Warren kicked in 17 and UCLA nearly doubled up the Flyers by halftime, leading 38-20.

What follows is a unique way of “scoring” results from the Winter Olympics.

This score is based on the “dominance” of each medal winner’s performance. It uses the performer’s Z Score based on his or her time or actual score in comparison with all other performers in the same event.

An average Z score for all athletes in any event would be approximately 0.00. The farther a score is from 0.00, the more exceptional it is. If a performance is timed, that exceptionality will be indicated by a negative figure; the more negative the Z Score, the more exceptional the performance. For events that are scored, the Z Score will be positive.

Accompanying each result is a scale indicating how it should be viewed based on historical norms. This will vary depending on the sport.

Here are results from Monday’s gold medal events in bobsled and speed skating. Scores for medal winners are included.

Bobsled

Historical norm: In bobsled, a Z Score lower than -1.72 is historically exceptional. A Z score between -1.20 and -1.71 is within the usual range for a gold medal. The best Z Score ever recorded in bobsled is -2.16, by the East Germany’s team in the 1976 men’s four-man event. The best American performance is -1.94 by the two-man team in 1936.

Two-man

Pos. Athlete, nation Time (Sec.) Z Score

Canada 86 -1.49

Germany 86 -1.49

Latvia 91 -1.43

Speed skating

Historical norm: In freestyle skiing, a Z Score lower than -2.40 is historically exceptional. A Z score between -1.50 and -2.40 is within the usual range for a gold medal. The best Z Score ever recorded in speed skating is -2.92, by Norway’s Johan Olav Koss in the 1994 5000 meters.

Men’s 500 meter speed skating

Pos. Athlete, nation Time (Sec.) Z Score

Havard Lorentzen, Norway 41 -2.17

Min Kyu Cha, Korea 42 -2.14

Tingyu Gao, China 65 -1.34

Scores from previous 2018 events

Women’s 500 meter speed skating

Pos. Athlete, nation Time (Sec.) Z Score

Nao Kodaira, Japan 94 -1.93

Lee Sang-Hwa, Korea 33 -1.42

Karolina Erbanova, Czech 34 -1.41

Men’s 10000 meter speed skating

Pos. Athlete, nation Time (Sec.) Z Score

Esmee Viser, Netherlands 23 -1.42

Martina Sablikova, Czech 85 -1.24

Natalia Voronna, Russia 98 -1.00

Men’s 10000 meter speed skating

Pos. Athlete, nation Time (Sec.) Z Score

Ted Bloemen, Canada 77 -1.13

Jorrit Bergsma, Netherlands 98 -1.01

Nicola Tumolero, Italy 32 -0.37

Women’s 1000 meter speed skating

Pos. Athlete, nation Time (Sec.) Z Score

Jorien Ter Mors, Netherlands 56 -1.91

Nau Kodaira, Japan 82 -1.70

Miho Takagi, Japan 98 -1.57

Men’s 1500 meter speed skating

Pos. Athlete, nation Time (Sec.) Z Score

Kjeld Nuis, Netherlands 01 -2.41*

Patrick Roest, Netherlands 86 -1.56

Min Seok Kim, Korea 93 -1.50

*Kjeld Nuis’ score of -2.41 equals the 10th best Z score in Olympic speed skating history, and is the third best in the history of the men’s 1500 meter race.

Women’s 1500 meter speed skating

Pos. Athlete, nation Time (Sec.) Z Score

1 Ireen Wust, Netherlands 114.35 -1.91

Miho Takagi, Japan 114.55 -1.80

Marrit Leenstra, Netherlands 115.26 -1.43

Men’s 5000 meter speed skating

Pos. Athlete, nation Time (Sec.) Z Score

1 Sven Kramer, Netherlands 369.76 -2.19

Ted-Jan Bloemen, Canada 371.60 -1.46

Sverre Lunde Pedersen, Norway 371.60 -1.46

Note: Kramer’s score of -2.19 is seventh-best in the history of the Olympic men’s 5000 meter race.

Women’s 3000 meter speed skating

Pos. Athlete, nation Time (Sec.) Z Score

Schtereekte, Netherlands 21 -1.55

Wust, Netherlands 29 -1.54

DeJong, Netherlands 02 -1.41

Alpine skiing

Historical norm: In alpine skiing, a Z Score lower than -2.20 is historically exceptional. A Z score between -1.60 and -2.19 is within the usual range for a gold medal. The best Z Score ever recorded in alpine skiing is -3.05, by Switzerland’s Madeleine Berthold in the 1956 women’s downhill. Curiously, women have historically dominated the best alpine skiing performances. The best by a male alpine skier was -2.56 by Hans Peter Burass of Norway in the 1998 slalom.

Scores from previous 2018 events

Men’s giant slalom

Pos. Athlete, nation Time (Sec.) Z Score

Marcel Hirscher, Austria 04 -2.75*

Henrik Kristoffersen, Norway 31 -1.48

Alexis Pinturault, France 35 -1.44

*Hirscher’s -2.75 Z Score is the fifth best in the history of Olympic alpine skiing. It is also the best Z Score ever produced by a male Olympic skier, surpassing the previous best of -2.57 by France’s Antoine Denarias in the 2006 downhill. The previous best Z Score in the men’s giant slalom was -2.40 by Austria’s Toni Sailor in 1956.

Women’s super giant slalom

Pos. Athlete, nation Time (Sec.) Z Score

Ester Ledecka, Czech 11 -1.41

Anna Veith, Austria 12 -1.40

Tina Wierthauer, Liechtenstein 22 -1.28

Men’s super giant slalom

Pos. Athlete, nation Time (Sec.) Z Score

Matteas Maier, Austria 44 -1.81

Beat Feuz, Switzerland 57 -1.63

Kjetil Jansrud, Norway 62 -1.56

Women’s slalom

Pos. Athlete, nation Time (Sec.) Z Score

Frida Hansdottir, Sweden 63 -1.88

Wendy Holdener, Switzerland 68 -1.84

Katharina Hallhuber, Austria 95 -1.66

Women’s giant slalom

Pos. Athlete, nation Time (Sec.) Z Score

Mikaela Shiffrin, USA 02 -1.50

Ragnhild Mowinckel, Norway 41 -1.31

Frederica Brignone, Italy 48 -1.28

Men’s downhill

Pos. Athlete, nation Time (Sec.) Z Score

Aksel Svindal, Norway 25 -1.88

Kjetil Jansrud, Norway 37 -1.75

Beat Fuez, Switzerland 43 -1.69

Men’s alpine combined

Pos. Athlete, nation Time (Sec.) Z Score

Marcel Hirscher, France 52 -2.01

Alexis Pinturault, France 75 -1.87

Victor Muffat-Jeandet, France 54 -1.36

Figure skating

Historical norm: In figure skating, a Z Score lower than -1.80 is historically exceptional. A Z score between -1.20 and -1.79 is within the usual range for a gold medal. The best Z Score ever recorded in figure skating is -2.69 by Peggy Fleming of the USA in the 1968 ladies.

Scores from previous 2018 events

Men’s singles

Pos. Athlete, nation Score Z Score

Yuzuru Hanyu, Japan 85 2.11*

Shomo Uno, Japan 90 1.69

Javier Fernandez, Spain 24 1.62

*Hanyu’s 2.11 Z Score is the ninth best by a figure skater in Olympic history. It is the second best by a male, trailing Yevgeny Plyuschenko in 2006.

Pairs

Pos. Athlete, nation Score Z Score

Savchenko/Massot, Germany 9 1.56

Sui/Han, China 47 1.53

Duhamel/Radford, Canada 15 1.22

Freestyle skiing/snowboarding

Historical norm: In freestyle skiing and snowboarding, a Z Score lower than -1.80 is historically exceptional. A Z score between -1.20 and -1.79 is within the usual range for a gold medal. The best Z Score ever recorded in freestyle skiing or snowboarding is -2.66, by Russia’s Vic Wild in the 2014 parallel slalom.

Men’s slopestyle

Pos. Athlete, nation Score Z Score

Oystein Braaten, Norway 00 1.01

Nick Goepper, USA 60 0.89

Alex Beaulieu-Marchand, Canada 4 0.79

Men’s aerials

Pos. Athlete, nation Score Z Score

Oleksandr Abramenko, Ukraine 51 1.03

Jia Zongyang, China 05 1.00

Ilia Burov, Russia 17 0.63

Scores from previous 2018 events

Women’s slopestyle

Pos. Athlete, nation Score Z Score

Sarah Hoeflin, Switzerland 20 1.45

Mathilde Gremaud, Switzerland 00 1.22

Isabel Atkin, Great Britain 60 0.97

Women’s aerials

Pos. Athlete, nation Score Z Score

Hanna Huskova, Belarus 14 1.22

Xin Zhang, China 52 1.19

Fanyu Kong, China 14 -0.03

Men’s halfpipe

Pos. Athlete, nation Score Z Score

Sean White, USA 97.75 1.69

Ayumu Hirano, Japan 95.25 1.51

Scott James, Australia 92.00 1.27

This is Shaun White’s third gold medal, and the lowest of his three Z Scores. White’s 2006 victory translated to a 2.38 Z Score, the third best performance in the history of freestyle skiing/snowboarding. His 2010 gold medal came on a 2.04 Z Score, the 12th best performance of all time.

Women’s halfpipe

Pos. Athlete, nation Score Z Score

Chloe Kim, USA 25 1.62

Jiyau Liu, China 75 1.08

Arielle Gold, USA 75 0.83

Women’s moguls

Pos. Athlete, nation Score Z Score

1 Perrine Laffont, France 78.65 0.96

Justine LaPointe, Canada 78.56 0.91

Yulia Galysheva, Kazakhstan 77.40 0.23

Men’s moguls

Pos. Athlete, nation Score Z Score

1 Mikael Kingsbury, Canada 86.63 0.70

Matt Graham, Australia 82.57 0.49

Daichi Hara, Japan 82.19 0.47

Men’s slopestyle

Pos. Athlete, nation Score Z Score

1 Redmond Gerard, USA 87.16 1.44

Max Parrot, Canada 85.20 1.09

Mark McManis, Canada 85.20 1.09

Women’s slopestyle/board

Pos. Athlete, nation Score Z Score

1 Jamie Anderson, USA 83.00 1.83*

Laurie Blouin, Canada 76.33 1.42

Enni Rukajarvi, Finland 75.38 1.36

*Jamie Anderson’s gold medal winning performance in the women’s slopestyle is the 22nd most dominant in the history of Olympic freestyle skiing/snowboarding competition.